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Composition operators between weighted Banach spaces of analytic functions

Published online by Cambridge University Press:  09 April 2009

J. Bonet
Affiliation:
Dept. Matemática Aplicada Univ. Politécnica de ValenciaE-46071 ValenciaSpain e-mail: [email protected]
P. Domański
Affiliation:
Faculty of Matematics and Comp. Sci. A. Mickiewicz University, ul. Matejki 48/49 60-769 PoznańPoland e-mail: [email protected]
M. Lindström
Affiliation:
Department of Mathematics Åbo Akademi University, FIN-20500 ÅboFinland e-mail: [email protected]
J. Taskinen
Affiliation:
Department of Mathematics P. O. Box 4, FIN-00014University of HelsinkiFinland e-mail: [email protected]
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Abstract

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We characterize those analytic self-maps ϕ of the unit disc which generate bounded or compact composition operators Cϕ between given weighted Banach spaces Hv or H0v of analytic functions with the weighted sup-norms. We characterize also those composition operators which are bounded or compact with respect to all reasonable weights v.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1998

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